The Saito-Kurokawa lifting and Darmon points

Let E_{/_\Q} be an elliptic curve of conductor $Np$ with $p\nmid N$ and let $f$ be its associated newform of weight 2. Denote by $f_\infty$ the $p$-adic Hida family passing though $f$, and by $F_\infty$ its $\Lambda$-adic Saito-Kurokawa lift. The $p$-adic family $F_\infty$ of Siegel modular forms admits a formal Fourier expansion, from which we can define a family of normalized Fourier coefficients $\{\widetilde A_T(k)\}_T$ indexed by positive definite symmetric half-integral matrices $T$ of size $2\times 2$. We relate explicitly certain global points on $E$ (coming from the theory of Stark-Heegner points) with the values of these Fourier coefficients and of their $p$-adic derivatives, evaluated at weight $k=2$.Comment: 14 pages. Title change

On px2+q2n=yppx^2 + q^{2n}= y^p and related Diophantine equations

The title equation, where $p>3$ is a prime number $\not\equiv 7 \pmod 8$, $q$ is an odd prime number and $x,y,n$ are positive integers with $x,y$ relatively prime, is studied. When $p\equiv 3\pmod 8$, we prove (Theorem 2.3) that there are no solutions. For $p\not\equiv 3\pmod 8$ the treatment of the equation turns out to be a difficult task. We focus our attention to $p=5$, by reason of an article by F. Abu Muriefah, published in this journal, vol. 128 (2008), 1670-1675. Our main result concerning this special equation is Theorem 1.1, whose proof is based on results around the Diophantine equation $5x^2-4=y^n$ (integer solutions), interesting in themselves, which are exposed in Sections 3 and 4. These last results are obtained by using tools such as Linear Forms in Two Logarithms and Hypergeometric Series.Comment: 23 pages, second version with minor revision

Pull out all the stops : textual analysis via punctuation sequences

Whether enjoying the lucid prose of a favourite author or slogging through some other writer’s cumbersome, heavy-set prattle (full of parentheses, em dashes, compound adjectives, and Oxford commas), readers will notice stylistic signatures not only in word choice and grammar but also in punctuation itself. Indeed, visual sequences of punctuation from different authors produce marvellously different (and visually striking) sequences. Punctuation is a largely overlooked stylistic feature in stylometry, the quantitative analysis of written text. In this paper, we examine punctuation sequences in a corpus of literary documents and ask the following questions: Are the properties of such sequences a distinctive feature of different authors? Is it possible to distinguish literary genres based on their punctuation sequences? Do the punctuation styles of authors evolve over time? Are we on to something interesting in trying to do stylometry without words, or are we full of sound and fury (signifying nothing)

The Fuchsian differential equation of the square lattice Ising model χ(3)\chi(3) susceptibility

Using an expansion method in the variables $x_i$ that appear in the $(n-1)$-dimensional integrals representing the $n$-particle contribution to the Ising square lattice model susceptibility $\chi$, we generate a long series of coefficients for the 3-particle contribution $\chi^{(3)}$, using a $N^4$ polynomial time algorithm. We give the Fuchsian differential equation of order seven for $\chi^{(3)}$ that reproduces all the terms of our long series. An analysis of the properties of this Fuchsian differential equation is performed.Comment: 15 pages, no figures, submitted to J. Phys.

Socio-occupational status and congenital anomalies

Background: The aim of this study is to investigate the association between socio-occupational status and the frequency of major congenital anomalies in offspring. Methods: The study population comprised 81 435 live singletons born to mothers enrolled in the Danish National Birth Cohort between 1996 and 2002. A total of 3352 cases of major congenital anomalies (EUROCAT criteria) were identified by linkage to the National Hospital Discharge Register. Malformations were recorded at birth or in the first year of life. Information about maternal and paternal socio-occupational status was collected prospectively using telephone interviews in the second trimester of pregnancy and was categorized as high, middle or low. Associations were measured as relative prevalence ratios using the highest socio-occupational status within the couple as the reference group. Results: The prevalence of all recorded major congenital anomalies was similar, about 4%, in all the socio-occupational categories. Low social status of the couple did, however, correlate with a higher prevalence of congenital anomalies of the ‘respiratory system’. No association was substantially attenuated when we adjusted for maternal and paternal age, smoking status, maternal alcohol habits, folic acid intake and body mass index. When malformations of the heart and the cardiovascular system were grouped together, they were more frequent in families where both parents presented a low socio-occupational status. Conclusion: We detected an association between low socio-occupational status and congenital anomalies of the respiratory system, the heart and the circulatory system. These malformations are good candidates for a large study on occupational, environmental and social determinants

Excesso de peso e obesidade abdominal em mulheres atendidas em Unidade da Estratégia Saúde da Família

Investigou-se a prevalência de excesso de peso e obesidade abdominal e variáveis associadas em mulheres. Estudo transversal com 298 mulheres (20-59 anos), usuárias de uma unidade da Estratégia Saúde da Família, em São Paulo-SP. Considerou-se o excesso de peso: índice de massa corporal>25kg/m²; a obesidade abdominal: circunferência da cintura 0,80m ou razão cintura-quadril>0,85. Realizou-se análise de regressão logística. O excesso de peso afetou 56% das mulheres, sendo 37% sobrepeso e 19% obesidade, e associou-se com a idade, renda familiar, tabagismo e hipertensão. 59% tinham obesidade abdominal associada à idade e hipertensão. Observou-sea elevada prevalência de excesso de peso e obesidade abdominal em mulheres, reforçando a importância da avaliação de circunferência da cintura e/ou razão cintura-quadril no exame físico, além do índice de massa corporal, auxiliadores da predição de risco. Evidencia-se a necessidade de intervenções, junto à comunidade, que promovam a diminuição do excesso de peso e da obesidade abdominal